Explain the statistical background behind power.

Statistical power is the probability of correctly rejecting the null hypothesis when it is false—i.e., detecting a true effect. In equation form:

Here, $β$ is the probability of a Type II error. Higher power increases the likelihood of finding a true effect.

Power depends on effect size, sample size, significance level ($α$), and population variance.

Smaller effect sizes require larger samples to detect an effect with the same power.

Power analysis is often conducted before a test to determine the minimum required sample size.